A369833 a(n) is the number of distinct values of the permanent of an n X n symmetric Toeplitz matrix using the first n prime numbers.

1, 1, 1, 6, 24, 120, 720, 5040, 40320, 362880

Offset: 0

Author

Stefano Spezia, Feb 03 2024

Keywords

• nonn
• hard
• more

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A000142, A351021, A351022.

Cf. A369830, A369831, A369832, A369834, A369835.

Programs

Mathematica

a[n_] := CountDistinct[Table[Permanent[ToeplitzMatrix[Part[Permutations[Prime[Range[n]]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]

Python

from itertools import permutations
from sympy import primerange, prime, Matrix
def A369833(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).per() for p in permutations(primerange(prime(n)+1))}) if n else 1 # Chai Wah Wu, Feb 11 2024

Formula

a(n) <= A000142(n).

Conjectured e.g.f.: 1/(1 - x) - x^2/2.